The monthly output p of a light bulb factory is given by the formula p = 450lk, where l is the amount invested in labor and k the amount invested in equipment (in thousands of dollars). if the company needs to produce 4,000 units per month, how should the investment be divided among labor and equipment to minimize the cost of production? the cost of production is l + k. (round your answers to the nearest cent.)investment in labor $investment in equipment $

C(p)  = 4,96 (in thousands of dollars)

l = 2980 $  invest in labor

k = 2980 $ invest in equipment

Step-by-step explanation:

Information we have:

Monthly output   P = 450*l*k       ⇒  k = P/450*l

But the production need to be 4000

Then k = 4000/450*l

Cost of production = l * k     (in thousands of dollars)

C(l)  =  l  + 4000/450*l

Taking derivatives (both members of the equation)

C´(l) = 1 - 400 /45*l²          ⇒ C´(l) = 0          ⇒ 1 - 400/45l²  = 0

45*l² -  400  = 0              ⇒  l²  = 400/45

l = 2.98 (in thousands of dollars)

l = 2980 $ And

k = 400/45*l           ⇒  k 400/45*2.98

k = 2.98  (in thousands of dollars)

C(p) = l + k

C(p)  =  2980 + 2980  

C(p)  = 5960 $

show us the picture

step-by-step explanation:

show the !

answer: - (a)

(b) 88 seats

step-by-step explanation:

given: in an auditorium, there are 22 seats in the first row and 28 seats in the second row.

thus first term=

second term=

the number of seats in a row continues to increase by 6 with each additional row.

⇒d= 6

a) given formula :

b)   let the number of seats (n) = 12

substitute n=12 in the explicit rule formed in (a)

∴there are 88 seats in 12 rows.